Theorems · Theorem · group theory
AddMonoidHom.eq_of_eqOn_denseM
∀ {M : Type u_1} {N : Type u_2} [inst : AddZeroClass M] [inst_1 : AddZeroClass N] {s : Set M},
AddSubmonoid.closure s = ⊤ → ∀ {f g : M →+ N}, Set.EqOn (⇑f) (⇑g) s → f = g- Defined in
- Mathlib.Algebra.Group.Submonoid.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddZeroClassAddZeroClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Top.topstatement and proof · cited by 9,680
- AddMonoidHomstatement and proof · cited by 3,230
- AddZeroClassstatement and proof · cited by 1,237
- AddSubmonoidstatement · cited by 1,178
- Set.EqOnstatement and proof · cited by 603
- AddSubmonoid.closurestatement and proof · cited by 224
- AddMonoidHom.eqOn_closureMproof · cited by 2
- AddMonoidHom.eq_of_eqOn_topMproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- AddMonoid.Coprod.hom_extproof · cited by 12
- Finsupp.addHom_extproof · cited by 6
- DFinsupp.addHom_extproof · cited by 4
- Polynomial.addHom_extproof · cited by 3
- PresentedAddMonoid.extproof · cited by 1